When centrifugal stretching is included in the energy for the states of the rigid rotor, equation has an extra term llind 2B(J, + 1) -4D(J, + 1), Equation (7-67), where J is the quantum number for the initial rotational state, B is the rotational constant and D is the centrifugal distortion constant. Use the data in Table 7.2to determine both B and D graphically. Be careful how you use units. Compare the magnitudes of B and D. What is the percent difference between B determinedwithout centrifugal stretching and that found here including centrifugal stretching? What would be the corresponding percent error in the bond length computedfrom 8?

In this question we have to answer some questions related to the centrifugal force.

Answered: When centrifugal stretching is included…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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work out the concentration profile c(r) of molecules in a centrifuge, which is Nelson's Eq. A sample is spinning at an angular velocity w (in radians/sec). The net mass or effective mass (as in our earlier lemonade problem) is mnet. From the view of molecules spinning at a distance r from the axis of spinning, there is an outwards force (the centrifugal force) f(r) = mnetw^2r (the same thing as mnetv2/r). You'll need to remember how this force gives you a potential energy that is seen by the molecules. It's this potential energy that should be used in a Boltzmann distribution. %3D
The greenhouse-gas carbon dioxide molecule CO2 strongly absorbs infrared radiation when its vibrational normal modes are excited by light at the normal-mode frequencies. CO₂ is a linear triatomic molecule, as shown in (Figure 1), with oxygen atoms of mass mo bonded to a central carbon atom of mass mc. You know from chemistry that the atomic masses of carbon and oxygen are, respectively, 12 and 16. Assume that the bond is an ideal spring with spring constant k. There are two normal modes of this system for which oscillations take place along the axis. (You can ignore additional bending modes.) In this problem, you will find the normal modes and then use experimental data to determine the bond spring constant. Figure O 1 mo 1x₁ 2 mc 1 of 1 3 mo 1Xz Part A Let x₁, x2, and 3 be the atoms' positions measured from their equilibrium positions. First, use Hooke's law to write the net force on each atom. Pay close attention to signs! For each oxygen, the net force equals mod²x/dt². Carbon has a…
Consider the hydrogen molecule H₂ as a rigid rotor with distance of separation of H-atoms r = 1.0 Å. Compute the energy of J = 2 rotational level.
The greenhouse-gas carbon dioxide molecule CO2 strongly absorbs infrared radiation when its vibrational normal modes are excited by light at the normal-mode frequencies. CO₂ is a linear triatomic molecule, as shown in (Figure 1), with oxygen atoms of mass mo bonded to a central carbon atom of mass mc. You know from chemistry that the atomic masses of carbon and oxygen are, respectively, 12 and 16. Assume that the bond is an ideal spring with spring constant k There are two normal modes of this system for which oscillations take place along the axis. (You can ignore additional bending modes.) In this problem, you will find the normal modes and then use experimental data to determine the bond spring constant. Figure O 1 mo T X₁ k C 2 mc 1X₂ k 1 of 1 > O 3 mo 1 X3 Part A Let ₁, 2, and 3 be the atoms' positions measured from their equilibrium positions. First, use Hooke's law to write the net force on each atom. Pay close attention to signs! For each oxygen, the net force equals mod²x/dt².…
In this and following questions, we develop a model for spontaneous emission of a photon by a diatomic molecule AB (a model molecule), which rotates and vibrates. In intermediate calculations, atomic units (a.u.) will be used: unit of mass = the mass of electron, unit of charge is the proton charge e, (e is a positive constant so that the charge of electron is -e). The initial state of the molecule is an excited rotational (1=1) and excited vibrational state (v=1). We consider a molecule with the reduced mass µ = 10,000 a.u. (it is similar to the mass of CO). After emitting a photon, the molecule will go to the 1=0, v=0 state. The first question is about the model potential of the molecule. It is represented by a potential of the form: V(r) = C6 p12 C12 p6 " where r is the distance between A and B in the molecule, C6 and C12 are positive constants (C6 =2 and C₁2-1). This potential has a well meaning that the molecule is bound. The first thing to do is find vibrational states of the…
A particle is confined to a two-dimensiona I ring of radius 100 pm. What are the wavelengths of the wavefunctions of the t hree lowest rotational levels?
Problem 1. The Morse potential, which is often used to model interatomic forces can be written in the form U(r) = D(1-e²²(²-))² 3 wherer is the distance between the two atomic nuclei. Determine the "spring constant" for small displacements from equilibrium for the Morse potential.
A particle is confined to a two-dimensiona l ring of radius 100 pm. What are the wavelengths of the wavefunctions of the t hree lowest rotational levels?
Hep structure. Show that the cla ratio for an ideal hexagonal close-paeked struc- ture is G) = 1.633. If cla is signifieantly larger than this value, the crystal structure may be thought of as composed of planes of closely packed atoms, the planes being loosely stacked. 1/2
Set up the relevant equations with estimates of all missing parameters. The molecular bond (spring constant) of HCl is about 470 N/m. The moment of incrtia is 2.3 x 10-47 kg-m². (a) At 300 K what is the probability that the molecule is in its lowest excited vibrational state? (c) Of the molecules in the vibrational ground state what is the ratio of the number in the gronnd rotational state to the number in the first excited rotational state?
Draw a typical dispersion relation curve (w-k curve ) for Vp=Vg and Vp not equal to Vg where Vp is the phase velocity and Vg the group velocity . Also the image for the delta w and delta k values are attached in a photo below . There are 9 values .
Question 6: The dispersion relation of a system is given by w(k) = 2w, sin, where wo is a constant and n is an integer. 1. Calculate the group velocity vg. 2. Calculate the phase velocity Uph.

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